The Osbournes may be America’s favorite dysfunctional family, but Upper East Side residents have mixed emotions when it comes to welcoming them as possible neighbors.

The Prince of Darkness and his kooky kin have been thwarted in their efforts to buy a $7 million, 48th-floor spread with 360-degree views in the Trump Palace condominium at 200 E. 69th St., owned by Donald Trump. “Their application listed three dogs,” said a Trump Palace insider. “The building no longer allows new dogs on the premises. Only the ones that were here when the rules changed can stay.”

Sources say Sharon Osbourne appealed to The Donald himself for an exception, to no avail.

So they’ve turned to music CEO Tommy Mottola – whose Epic label features the Osbourne Family Album – as their ambassador to the neighborhood. Mottola, who owns a massive townhouse on East 64th Street, is said to have made several calls to brokers on behalf of the Osbournes, whose unusual home life has been featured in a top-rated MTV show. But being connected is not always the key to a key on the Upper East Side.

“That television show is outrageous,” said one Park Avenue condominium owner. “I’ve only seen it a couple of times, but the family seems kind of crazy.”

Others who reside on the Upper East Side – one of Manhattan’s wealthiest neighborhoods – appear more charitable toward the aged rocker and his family.

“He [Osbourne] would certainly cause a lot of excitement in the building,” said one resident of Trump Tower on Fifth Avenue at 55th Street, who requested anonymity.

Patrick Tierney, the resident manager at tony 515 Park Ave., whose residents include Vivendi CEO Jean-Marie Messier, music producer Antonio “L.A.” Reid and Broadway theater scion James Nederlander, is among those who said he would have “no problems” with the Osbournes moving into the building.

Not welcome, he added, would be around-the-clock cameras.

“Filming is definitely not allowed in the building because it would interrupt the lifestyle and comfort of the other residents,” Tierney said.

Trump Tower might be a better choice for Ozzy. The building has seen its share of cameras filming the building’s many celebrities. It’s also where Michael Jackson spent his honeymoon with Lisa Marie Presley. The Osbournes might be tame by comparison.